I used my bread machine on the dough setting to do most of the work. I put in the ingredients, walked away for 1:45, and came back to dough that was ready to cut and shape. Since meeting its untimely demise last year, I don't have a baking stone, and just used the bottom of a regular baking sheet to bake the pitas.
While in the oven, these were really puffy, although they deflated pretty quickly upon coming out. Some of them had great pockets for sandwiches, and on the others, we just used the two halves and put the sandwich fillers in between. These were light and fluffy, and had no weird aftertastes. And it's cheap. (Pita bread is so expensive around here.)
The recipe is available at the King Arthur Flour site. Enjoy!